1. The real variable function is a generalization of Riemann integral. This paper introduces a new integral-Lebesgue integral, which expands the scope of integrable functions.
2. It is worth noting that Newton's Leibniz formula is not necessarily true in Lebesgue integral (only one symbol is less than or equal to), unless it is absolutely continuous or bounded variation.
3. In the process of introducing Lebesgue integral, measure theory is essential, and there are many ways to introduce measure.
It is no problem to master these basic logics, and no preparatory knowledge is needed. Usually, a real change book should have some knowledge of set theory.
5. Advanced algebra, analytic geometry, differential equations and complex variables are completely useless, and they are basically mathematical analysis.